Line shapes in pump-probe spectroscopy of polaritons

Forming new hybrid quasiparticles by strong light-matter coupling is a promising tool for tailoring the photophysics and photochemistry of molecules. Thus, the ultrafast dynamics of polaritons formed upon strong light-matter coupling has been extensively studied by pump-probe spectroscopy. Although it was predicted that the partial photonic character of polaritons should shorten their lifetime compared to purely molecular excited states, many studies do not observe this effect. So far, the unexpected longevity of the spectral signatures has been either explained by relaxation into a manifold of so-called dark states or by other uncontrolled effects that change the properties of cavity materials. In order to resolve these issues, we investigate here the dependence of the line shape of pump-probe spectra of polaritons on the ratio of photonic and molecular character. Furthermore, by phenomenologically including relaxation to dark states, we find that it is possible to spectrally resolve this relaxation process by observing a characteristic phase flip in the pump-probe signal. Our results show that the signatures of dark state relaxation and the influence of the cavity resonance energy and their contributions to the polariton dynamics can be disentangled from the spectral line shapes.